thesis_2012_09_07_final_must read.pdf

8/17/2019 Thesis_2012_09_07_Final_MUST READ.pdf

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IMPERIAL COLLEGE LONDON

USE OF MICROWAVES FOR THE

DETECTION OF CORROSION UNDER

INSULATION

by

Robin Ellis Jones

A thesis submitted to Imperial College London for the degree of

Doctor of Engineering

Department of Mechanical Engineering

Imperial College London

London SW7 2AZ

April 2012


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Declaration of originality

The material presented in the thesis “Use of Microwaves for the Detection of Corro-

sion Under Insulation” was composed and originated entirely as a result of my own

independent research under the supervision of Dr. Francesco Simonetti and Prof.

Michael Lowe. All published or unpublished material used in this thesis has been

given full acknowledgement.

Robin Ellis Jones

18th April 2012


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Abstract

Corrosion Under Insulation (CUI) is a widespread problem throughout the oil and

gas industry, and is a major cause of pipeline failure. CUI occurs on pipelines fitted

with thermal insulation; the insulation itself is protected from the environment by

a layer of metallic cladding and sealed to prevent water ingress. This cladding

can deteriorate from age or become damaged, allowing the ingress of water into

the insulation, which allows corrosion of the external pipe surface to initiate. This

corrosion can proceed at an accelerated rate due to the elevated process temperature

of the pipe, compromising the integrity of the pipeline. The detection of this typeof corrosion is an ongoing problem for the oil and gas industry, as the insulation

system conceals the condition of the pipe. Therefore, there is a requirement for a

long-range, screening inspection technique which is sensitive to the first ingress of

water into the insulation, in order to provide an early warning of areas of a pipeline

at risk from CUI.

This thesis describes the development of a new inspection technique which employs

guided microwaves as the interrogating signal. Such guided microwaves provide a

means of screening the length of a pipeline for wet insulation, by using the structure

of a clad and insulated pipeline as a coaxial waveguide to support the propagation of

electromagnetic waves. Areas of wet insulation will create impedance discontinuities

in the waveguide, causing reflections of the incident microwave signal, allowing the

water patches to be detected and located. The performance of such a guided wave

inspection system is intrinsically linked to the signal-to-coherent-noise ratio (SCNR)

that can be achieved. Therefore, the value of the SCNR that the technique is

capable of achieving is of central importance to this thesis. The excitation system is

optimised to maximise the SCNR, whilst the effect of typical pipeline features such

as bends, pipe supports and the various types of insulation which can be used, are

studied to quantify the effect on the SCNR.

A wide variety of methods are employed throughout the development of the guided

microwave technique described in this thesis. Theoretical methods are employed in

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the initial stages to enable the development of a model to describe electromagnetic

wave propagation in the large coaxial waveguides formed by pipelines. Numerical

simulation techniques are employed when there are too many parameters to study

for experimentation to be a viable option, and to study complex problems for which

no analytical solution exists. Experiments are conducted in the laboratory using

a model setup which employs metallic ducting to represent an insulated pipeline.

These experiments are performed to demonstrate the practical feasibility of the

technique, and to study pipeline features in a controlled environment. Finally, ex-

periments are performed in the field on a section of real industrial pipeline, in order

to validate the accuracy of the model experimental setup in representing conditions

which exist on real pipelines.

The main findings of the thesis are that it is possible to excite a guided microwave

signal in a large coaxial waveguide with a high SCNR. Experiments revealed that

the technique is highly sensitive to the presence of water in the waveguide. Measure-

ments of the effect of different types of insulation demonstrated that rockwool causes

a very low attenuation of the microwave signal, while polyurethane foam insulation

has a slightly higher attenuation coefficient. An investigation into the effect of bendsdetermined that, whilst significant mode conversion occurs at a bend, the transmis-

sion coefficient of the TEM mode is high for typical bend angles and bend radii in

small diameter pipes. The behaviour of the signal at a typical pipe support was

also examined; the reflection from the support was minimal, whilst the transmission

beyond the support remained relatively high. Whilst there is still further work to be

done before this technique can be applied in the field, the major aspects of practical

implementation that could affect the technique have been investigated here, and theresults consistently indicate the feasibility of the technique for long-range screening

of insulated pipelines for water.

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Acknowledgements

There are many people I would like to thank for their contribution to this thesis. I

am very grateful to Francesco Simonetti for his flawless supervision and insightful

guidance, which, not only taught me so much, but made the whole process immensely

enjoyable. My gratitude also goes to Mike Lowe and Ian Bradley, for their invaluable

contributions at every stage of this project, and for their help in making things

happen.

I would like to thank Chris Scruby for his wise counsel, and for offering me the

EngD opportunity in the first place. I would like to express my appreciation of

the accomplishment of Peter Cawley, Mike Lowe, and Fred Cegla in making the

NDT research group such a stimulating and enjoyable environment within which

to conduct research. I must also thank everyone who has ever helped me move

awkward pieces of ducting around for my experiments: I think this must be almost

everyone to have stepped into the lab over the past few years! My gratitude also

goes to David Tomlin and Phil Wilson for their time and expertise in machining.

At BP, I would like to thank Simon Webster, Tom Knox, Danny Keck and Ian

Bradley for their insights and suggestions at various stages of the project’s devel-

opment. I am also grateful to BP for their financial support of this project, in

particular, investing in the experimental hardware. I would also like to acknowl-

edge the financial support of EPSRC, through the Centre for Doctoral Training in

Non-Destructive Evaluation.

On a less industrious note, I would like to thank Johnny, Dom, and Joe for their

friendship and their belaying, and an excellent time exploring the Indian Himalayas;

my compatriots in the 2007 EngD cohort: Sam, Kit, Gabriel, Keith, Chris, and

Christiaan, for making our courses so enjoyable; and my colleagues in the NDT lab

at Imperial, for countless intriguing discussions and good times at the conferences

in the USA.

I would like to express my deepest gratitude to my family: my mum for being so

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willing to listen to me talk about my work in gruesome detail; my dad for all of his

invaluable solutions to practical problems, which were invariably spot-on; and Chris

and Hannah for introducing me to my wonderful nephews Riley and Henry. Finally,

I would like to thank Delphine for her unwavering support and generosity of spirit.

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Contents

1 Introduction 28

1.1 Mechanism of Corrosion Under Insulation . . . . . . . . . . . . . . . 29

1.2 Non-Destructive Evaluation Techniques for the Detection of CUI . . . 32

1.3 The Premise for the Use of Microwaves for the Detection of CUI . . . 35

1.4 Similar Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

1.5 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2 Theoretical Background 42

2.1 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.2 Analytical Solution for the Rectangular Waveguide . . . . . . . . . . 45

2.3 Numerical Techniques to Study Complex Problems . . . . . . . . . . 53

2.4 Synthetic Time-Domain Reflectometry . . . . . . . . . . . . . . . . . 54

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3 Coaxial Waveguide Theory 57

3.1 Assumptions Made by the Model . . . . . . . . . . . . . . . . . . . . 58

3.1.1 Transparent Insulation . . . . . . . . . . . . . . . . . . . . . . 58

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CONTENTS

3.1.2 Perfectly Conducting Waveguide . . . . . . . . . . . . . . . . 60

3.2 The Analytical Solution Used by the Model . . . . . . . . . . . . . . 61

3.3 Design of a Guided Wave Inspection System . . . . . . . . . . . . . . 73

3.3.1 Non-Dispersive Propagation . . . . . . . . . . . . . . . . . . . 73

3.3.2 Mode Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.3.3 Frequency Bandwidth . . . . . . . . . . . . . . . . . . . . . . 74

3.4 Use of an Array of Antennas . . . . . . . . . . . . . . . . . . . . . . . 75

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4 Antenna Array Design 79

4.1 Monopole Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.2 Preliminary Antenna Array Design . . . . . . . . . . . . . . . . . . . 81

4.3 Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.3.1 Potential Impedance Matching Methods . . . . . . . . . . . . 84

4.3.2 Impedance Matching with Antenna Design . . . . . . . . . . . 86

4.4 Simulations to Optimise Antenna Array . . . . . . . . . . . . . . . . 87

4.4.1 Methods for Using MWS to Simulate an Antenna Array . . . 88

4.4.2 Optimisation of Antenna Design . . . . . . . . . . . . . . . . . 90

4.5 Array Designs for Various Pipeline Specifications . . . . . . . . . . . 92

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5 Experimental Validation of the Technique 97

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CONTENTS

7.1.1 The Bend Model . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.1.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 139

7.1.3 Effect of Pipeline Dimensions . . . . . . . . . . . . . . . . . . 144

7.2 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . 146

7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

8 The Effect of Pipe Supports 154

8.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

8.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

8.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

9 Conclusions 161

9.1 Review of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

9.2 Summary of Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

9.2.1 Achieving a High Signal-to-Noise Ratio . . . . . . . . . . . . . 164

9.2.2 High Sensitivity to Water . . . . . . . . . . . . . . . . . . . . 165

9.2.3 Robustness to Pipeline Conditions . . . . . . . . . . . . . . . 166

9.2.4 Implementation of the Guided Microwave Technique . . . . . . 169

9.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

A Optimisation of an Antenna in a Rectangular Waveguide 175

B Calculation of Dispersion Curves for Modes in Bends 178

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List of Figures

1.1 On the 29th September 2008 a high pressure gas pipeline ruptured at

Prudhoe Bay, causing a release of natural gas into the atmosphere,and launching two sections of pipe into the air to land 900 feet away

from the incident [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.2 The structure of a clad and insulated pipeline can be used as a

large coaxial waveguide to support the propagation of electromag-

netic waves. The microwave regime is of particular interest due to

the sensitivity of these frequencies to the presence of water, raising

the possibility of being able to detect the first ingress of water into

the insulation, allowing the initiation of corrosion to be prevented. . . 36

1.3 Antennas are inserted into the insulation layer, exciting microwave

propagation down the length of the pipeline. Water volumes in the

insulation act as impedance discontinuities, giving rise to a partial

reflection of the incident signal which can be used to detect and locate

wet sections of insulation along the length of the pipeline. . . . . . . . 37

2.1 Cross-sectional view of a rectangular waveguide. The dimensions of

the waveguide are denoted by w for the width, and h for the height. . 45

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LIST OF FIGURES

2.2 Phase and group velocity dispersion curves, normalised to the speed

of light in vacuum, for some of the lower modes in a G band rectan-

gular waveguide (dimensions of w = 47.5mm and h = 22.1mm and

a frequency range of 3.95 to 5.85 GHz bandwidth). . . . . . . . . . . . 47

2.3 Phase velocity dispersion curves for two standard sizes of rectangular

waveguide. It can be seen that each waveguide is capable of sup-

porting the propagation of only the TE10 mode within its operating

frequency range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.4 Field patterns for the nine lowest modes that exist in a rectangular

waveguide with w/h = 2. . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.1 Schematic diagram of the cross-section of a coaxial waveguide. The

radius of the outer conductor is referred to as a, whilst the radius of

the inner conductor is b. . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.2 Phase and group velocity dispersion curves, normalised to the speed

of light in vacuum, for some of the lower modes in a coaxial waveguidewith dimensions of a = 157.5mm and b = 80 mm. Only the modes

up to TM44 and TE44 are plotted, for clarity. . . . . . . . . . . . . . . 64

3.3 Phase velocity dispersion curves for the lowest modes in coaxial waveg-

uides. Figures (a), (c), and (e) show the effect of increasing the radius

of the inner pipe, whilst (b), (d), and (f) show the effect of increasing

the thickness of the insulation. . . . . . . . . . . . . . . . . . . . . . . 65

3.4 Field patterns for fifteen of the modes that exist in coaxial waveguides. 69

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LIST OF FIGURES

3.5 Diagram illustrating the unwrapping of the coaxial annulus. The

average radius of the coaxial waveguide is denoted by s, giving a cir-

cumference of 2πs, and the annular distance is denoted by d. The

wavenumber vector, k, has radial and circumferential coordinates

given by kr and kθ. At the cutoff frequency of a mode, the wavenum-

ber vector is contained in the plane of the cross-section of the wave-

guide, and the two dashed boxes in the Figure will coincide. . . . . . 71

3.6 Diagram illustrating the use of an antenna array to suppress non-

axisymmetric modes. The diagrams on the left represent the mode

structures of the modes: TE11 and TE41. The diagrams on the right

provide an unwrapped representation of how the electric field of these

modes varies about the circumference of the waveguide; the TE11

mode has one cycle of variation, whilst the TE41 has four cycles of

variation about the circumference. With two antennas per cycle,

any positive electric field amplitude is cancelled by the corresponding

signal measured by the next antenna positioned a half cycle around

the circumference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.1 Diagram of a junction between a coaxial line and a rectangular wave-

guide using a probe antenna to couple the electric fields. . . . . . . . 80

4.2 Diagram of a monopole antenna and a dipole antenna, which have

identical radiation patterns. . . . . . . . . . . . . . . . . . . . . . . . 81

4.3 (a) Photograph of the design employed for the preliminary antennas.(b) Photograph of the full array of eight antennas. . . . . . . . . . . . 82

4.4 Diagram of the experimental setup used in the preliminary experi-

ment. The VNA is connected to the 8-way splitter that divides the

signal into the eight channels required to feed the array of eight an-

tennas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

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LIST OF FIGURES

4.5 The signal from the preliminary antenna design. The signal has a

low SCNR due to the poor impedance match at the antennas, which

prompted an investigation into possible methods of matching the

impedance of the antenna array to the coaxial cables feeding the array. 85

4.6 Model of a six-antenna array used to excite a large coaxial wave-

guide formed from an annular vacuum component in blue within a

perfectly electrically conductive background material. The feeding

cables incorporate a 90◦ bend in order to align the waveguide ports

(red squares) with the x-y plane. . . . . . . . . . . . . . . . . . . . . 89

4.7 Methods used to optimise the design of the antenna array: (a) dis-

plays the results of the initial approach, a two dimensional parameter

sweep; (b) displays the results using the pattern search optimisation

algorithm, which yields more accurate results and a 76 % saving in

time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.8 Figure displaying the optimum antenna designs for pipe diameters of

4, 6, 8, 12, 18, and 24 ” and insulation thicknesses of 1, 2, 3, and 4 ”.The optimum length is displayed on the z -axis, the optimum radius

is denoted by the size of the spot, with the value given in mm above

the spot, and the IMR of the antenna is given by the colour of the spot. 94

5.1 Photograph of the experimental setup used in the laboratory. Coax-

ially aligned lengths of ventilation ducting with a = 157.5mm and

b = 80 mm are used to represent a 6 ” pipe with 3 ” insulation. . . . . 99

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LIST OF FIGURES

5.2 Schematic diagram of the experimental setup used in the laboratory.

The waveguide is formed from an inner duct aligned coaxially within

the outer duct, both with a length of 3 m, and with short-circuiting

metallic end-caps fitted to both ends. A vector network analyser

generates the microwave signal; an 8-way splitter divides the single

channel into the eight required for the array; eight cables of equal

length (in order to preserve equality of phase) connect the splitter

outputs with the antennas of the array. The antennas are positioned

λm/4 = 78.5 mm from the proximal short-circuiting termination, for

constructive interference. . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.3 Photograph of the antenna fabricated according to the simulated opti-

mum design for a coaxial waveguide with a = 157.5 mm and b = 80 mm.101

5.4 Signal from the ducting equivalent to a 6 ” pipe with 3 ” insulation. . 102

5.5 Signal from the ducting equivalent to a 6 ” pipe with 2 ” insulation. . 103

5.6 Comparison of signals obtained with a single antenna and a complete

array of eight antennas. The improvement in the SCNR with the use

of an array provides validation for the array approach used in the

excitation system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.7 Photographs of three of the main insulation types used industrially:

(a) rockwool, (b) polyurethane foam, (c) glass foam. . . . . . . . . . . 105

5.8 Signals measuring the attenuation of rockwool insulation. . . . . . . . 107

5.9 Signals measuring the attenuation of polyurethane foam insulation. . 109

5.10 Signals measuring the attenuation of glass foam insulation. . . . . . . 110

5.11 Photos from the field tests: (a) the section of real industrial pipeline,

with removable cladding cover to provide access to the insulation; and

(b) the equipment used to take the readings. . . . . . . . . . . . . . . 113

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LIST OF FIGURES

5.12 Comparison of a signal recorded during the field test on a 5 m length

waveguide with a signal recorded using the model laboratory setup of

a 6 m length waveguide. The difference in the lengths of the waveg-

uides tested gives rise to the difference in the arrival times of the

end reflections. Excellent agreement is demonstrated between the

two, providing validation for the accuracy of the laboratory setup in

representing the conditions which exist on a real insulated pipeline. . 114

6.1 Reproduced from Figure 7.9 in Jackson [32, p.315]. Index of refrac-

tion (top) and absorption coefficient (bottom) for liquid water as a

function of frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.2 Diagram of the rectangular toroidal tank, positioned within the coax-

ial waveguide, which was used in simulations to assess the strength

of reflection from increasing volumes of water. . . . . . . . . . . . . . 122

6.3 Simulated reflection coefficient of the TEM mode, propagating in a

coaxial waveguide with a = 157.5 mm and b = 80 mm, as a function

of the cross-sectional area of the waveguide occupied by water. The

axial extent of the water volume is 50 mm. . . . . . . . . . . . . . . . 123

6.4 Experimental setup. The VNA generates the microwave signal, which

is split into eight channels by the splitter to feed the array. The

ducting is short-circuited at both ends. The toroidal tank is placed

in the centre of the waveguide, with a hose running through a hole in

the ducting to introduce discrete volumes of water into the tank. . . . 124

6.5 The toroidal tank placed in the centre of the waveguide and gradually

filled with discrete volumes of water, in order to determine the sensi-

tivity of the technique to the presence of water within the waveguide. 126

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LIST OF FIGURES

6.6 Signals measured for four water volumes: (a) 0, (b) 200, (c) 500, and

(d) 1000 ml. The water volume is positioned 1.5 m from the array.

The signals are normalised to the amplitude of the reflection from

the end of the empty waveguide. As the water volume increases,

so does the amplitude of the reflection from it, while the reflection

from the end of the waveguide decreases by energy conservation and

attenuati on. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.7 Reflection coefficient as a function of cross-sectional extent of the

waveguide occupied by water inside a ring torus tank. Experimental

results are compared to numerical simulations. . . . . . . . . . . . . . 128

6.8 Photograph showing three wet insulation sections placed within the

waveguide before the removable cover is replaced. . . . . . . . . . . . 129

6.9 Four examples of signals from the field tests: (a) no wet insulation;

(b) one section of wet insulation, equivalent to 12.5 % cross-sectional

extent; (c) four wet insulation sections, equivalent to 50 % cross-

sectional extent; and (d) all eight wet insulation sections, equivalentto 100 % of the cross-section of the waveguide annulus occupied by

wet i nsul ati on. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.10 The reflection coefficient of the wet insulation as a function of the

cross-sectional extent of the insulation annulus that is occupied by

wet insulation. Field test data is plotted alongside results obtained

from simulations and results from a previous laboratory experiment;

the three data sets are in good agreement. . . . . . . . . . . . . . . . 131

6.11 The reflection coefficient of the TEM mode from a transition interface

between dry and wet insulation, as a function of the length of the

transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

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LIST OF FIGURES

7.1 (a) Circular waveguide with the low-loss TE01 mode in excitation into

a bend, which undergoes mode conversion such that a proportion of

the energy emerges in the TM11 mode. (b) Diagram showing how

the extent of the mode conversion in a circular waveguide oscillates

sinusoidally as a function of the bend angle, with maximum mode

conversion occurring at an angle φc. . . . . . . . . . . . . . . . . . . . 136

7.2 Coaxial waveguide with the TEM mode in excitation; it is expected

that there will be mode conversion with a proportion of the energy

emerging in the modes of the TE p1 mode family (TE11, TE21, etc.). . 137

7.3 Mode conversion in transmission as a function of the bend angle. The

amplitudes of the transmitted TEM mode and the first three members

of the TE p1 mode family are normalized relative to the amplitude

of the incident TEM mode. The radius of the outer conductor is,

a = 157.5 mm, and the radius of the inner conductor is, b = 80mm.

The bend radius is R = 1260 mm (4D), which is representative of the

curvature of bends found industrially. . . . . . . . . . . . . . . . . . . 140

7.4 Comparison of the modal amplitude of the transmitted TEM mode

as a function of bend angle for bend radii increasing from 0.5D to

10D. The extent of mode conversion is greater for sharper bends. . . . 141

7.5 (a) Frequency-wavenumber dispersion curves displaying the modal

components which propagate inside a 1D bend, despite only the TEM

mode being excited. (b) Dispersion curves for a 1D bend and a 2D

bend. From comparison with the dispersion curves for the straight

waveguide, it can be seen that phase velocity of the modes is affected

by the curvature of the bend, in particular the TEM mode becomes

dispersive. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

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LIST OF FIGURES

7.6 The TEM transmission coefficient as a function of pipe diameter and

insulation thickness for bend angles of 45◦ (top plots) and 90◦ (bottom

plots), and for bend radii of 3D (left-hand plots) and 5D (right-hand

plots). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.7 Plots displaying the TEM transmission coefficient as a function of

bend angle for 3D and 5D bends in pipes with diameters of 4, 8, and

24 ” pipes with 2 ” of insulation. As the pipe diameter increases, the

extent of the mode conversion increases, whilst the periodicity of the

oscillation of energy between the modes becomes shorter. . . . . . . . 146

7.8 This experimental validation uses the same equipment as in previous

experiments. Two straight 3 m lengths of ducting were connected by

a 1 m length of flexible metallic ducting, allowing the angle of the

bend to be v ari ed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

7.9 Diagram of the experimental setup used to investigate the effect of

varying bend angle on the transmission coefficient of the TEM mode. 148

7.10 Three examples of signals obtained from this experiment; bend angles

of 0◦, 45◦, and 90◦ are shown. The left-hand plots display the pulse-

echo signals obtained from the S11 scattering parameter, whilst the

right-hand plots display the pitch-catch signals from the S21 scattering

parameter. It can be seen that increasing the bend angle does not

cause peaks to appear in the region of the bend, which means that

bends do not cause any significant reflection. . . . . . . . . . . . . . . 149

7.11 Experimentally measured transmission coefficient of the TEM mode

versus bend angle, including comparison with numerical simulations.

The excellent agreement between the datasets provides validation for

the accuracy of the simulations. . . . . . . . . . . . . . . . . . . . . . 150

8.1 Schematic diagram of the experimental setup used to investigate the

effect of pipe supports in the waveguide. . . . . . . . . . . . . . . . . 156

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LIST OF FIGURES

8.2 Photo of experimental setup used to investigate the effect of pipe

supports in the waveguide. . . . . . . . . . . . . . . . . . . . . . . . . 157

8.3 Three examples of signals from the experiment in which the length of

the pipe support was varied. These signals are for support lengths of

0 mm (empty waveguide), 300 mm, and 500 mm. The left-hand plots

display the pulse-echo signals, whilst the right-hand plots display the

pitch-catch signals. In the pitch-catch signals, the peak at 3.5 m is

used to determine the amplitude of the signal transmitted beyond the

support. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

8.4 The transmission and reflection coefficients of the TEM mode as a

function of the length of a pipe support with a thickness of 10 mm

and a height equivalent to the annular spacing. Experimental data is

compared to results obtained from simulations, and shown to be in

good agreement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

A.1 Results from two experiments conducted using rectangular waveguide,

to determine whether the design of the antenna could be used to im-

prove the impedance matching at the junction between a coaxial cable

and a waveguide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

B.1 Modal components propagating inside the bend. The frequency-

wavenumber dispersion curves are obtained by measuring the total

electric field along the bend length and performing a 2-D Fourier

transform in time and space. The curves refer to a sharp 1D bend

and the gray scale provides an indication of the modal amplitude.

Only the TEM mode was excited; the presence of three additional

modes indicates that there are multiple modes propagating in a coax-

ial toroid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

20


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LIST OF FIGURES

B.2 Effect of the bend radius on the dispersion characteristics of the modes

propagating in a coaxial toroid with inner and outer radii 80 mm and

157.5 mm, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . 181

21


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List of Tables

3.1 Table listing the values of the resistivity and conductivity of typical

pipeline materials. Pipes are typically formed from carbon or stainlesssteel, whilst cladding can be stainless steel, galvanised carbon steel

or aluminium. Kaye and Laby [52, p.150] provided these values. . . . 60

4.1 Table listing the pipeline diameters for which optimum antenna de-

signs were obtained, accompanied by the number of antennas required

in each case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.2 Table giving the optimum antenna designs, in terms of the optimum

length (as a fraction of the annular distance), optimum radius, and

resultant IMR, for pipes with diameters of 4, 6, 8, 12, 18, and 24 ”

and insulation thicknesses of 1, 2, 3, and 4”. . . . . . . . . . . . . . . 93

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List of Symbols

α Attenuation coefficient

β̄ Phase constant normalised to that of vacuum

F̄ Average of two cutoff frequencies

β Phase constant

∆F Difference between two cutoff frequencies

δ Skin depth

Permittivity

0 Vacuum permittivity

∞ Infinite frequency relative permittivity

r Relative permittivity

r Real part of permittivity

r Imaginary part of permittivity

s Static relative permittivity

Γ Reflection coefficient

γ Ratio of inner and outer conductors of coaxial waveguide, a/b

κ Thermal conductivity

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List of Symbols

λ Wavelength

λ0 Wavelength in vacuum

λm Centre wavelength

λr, λθ Cylindrical components of wavelength

λwg Wavelength inside a waveguide

µ0 Vacuum permeability

µr Relative permeability

ν g Group velocity

ν p Phase velocity

ω Angular frequency

φ Angular extent of a bend

φc Bend angle of maximum mode conversion in cylindrical waveguide

ρ Electrical resistivity

σ Electrical conductivity

τ Relaxation time of a polar molecule

B Magnetic flux density

D Electric flux density

E Electric field

H Magnetic field

J Conduction current density

k Wavenumber vector

ξ Solution to Equation (3.3) or (3.4) for a mode ( p, q )

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List of Symbols

a Radius of outer conductor of coaxial waveguide

A1, A2 Amplitudes used to calculate attenuation coefficient

b Radius of inner conductor of coaxial waveguide

c Speed of light in a dielectric medium

c0 Speed of light in vacuum

d Annular distance of coaxial waveguide, a − b

f Frequency

f c Cutoff frequency

f m Centre frequency

F p,q Cutoff frequency of the T p,q mode

h Height of rectangular waveguide

j Imaginary unit,√

−1

J p Bessel function of first kind of order p

J p Prime notation denotes differentiation of the Bessel function

k Wavenumber

kr, kθ Cylindrical components of wavenumber vector

kx, ky Cartesian components of wavenumber vector

l Length of coaxial waveguide

l1, l2 Lengths of coaxial waveguides used in simulations

n Index of refraction

p Modal order integer in x direction for rectangular waveguides, and in θ

direction for coaxial waveguides

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List of Symbols

Q Free charge density

q Modal order integer in y direction for rectangular waveguides, and in r

direction for coaxial waveguides

R Radius of curvature of a bend

r,θ,z Cylindrical coordinates

s Average radius of coaxial waveguide, (a + b)/2

t Time

T p,q A mode of the coaxial waveguide

w Width of rectangular waveguide

x,y,z Cartesian coordinates

X p A combination of Bessel functions, according to Equation (3.9)

Y p Bessel function of second kind of order p

Z 0 Characteristic impedance

Z p A combination of Bessel functions, according to Equation (3.12)

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List of Abbreviations

CUI Corrosion Under Insulation

FIT Finite Integration Technique

IMR Impedance Matching Ratio

MWS Microwave Studio

NDE Non-destructive Evaluation

NPS Nominal Pipe Size

PEC Perfect Electrical Conductor

PTI Profile Technologies Incorporated

PUF Polyurethane Foam

QNDE Quantitative Non-destructive Evaluation, Review of progress in

SCC Stress Corrosion Cracking

SCNR Signal-to-Coherent-Noise Ratio

SMA Sub-Miniature version A

TE Transverse Electric

TEM Transverse Electromagnetic

TM Transverse Magnetic

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Chapter 1

Introduction

At 12.30pm on Monday the 29th September 2008 a high-pressure gas pipeline rup-

tured at the Prudhoe Bay oil field in Alaska [1]. The pipeline burst, propelling two

sections of pipe, 14 feet and 28 feet in length, 900 feet across the tundra [2, 3], as

shown in Figure 1.1. The gas line was isolated and depressurised after about an

hour, however, this allowed natural gas to be released into the atmosphere, which

could have led to an explosion. No injuries to personnel were sustained in this inci-

dent, nor was there any spillage or fire or explosion, however, the potential for any

of these to have occurred was great. The requirement to shut down production on

a sector of the Prudhoe Bay oil field led to an economic impact in terms of lost pro-

duction, in addition to the fact that a release of gas into the atmosphere can incur

a hefty fine from the regulating bodies [1]. The cause of this failure was Corrosion

Under Insulation (CUI).

Corrosion under insulation is a major problem throughout the oil and gas industry,

but it is not only the petrochemical industry which is affected; CUI is also a problem

for the power and manufacturing industries, but can occur wherever pipelines are

fitted with thermal insulation. It is a problem which is not isolated to a particular

geographical location; it occurs in facilities and on pipelines all over the world. This

form of corrosion occurs on steel pipelines which have been fitted with thermal insu-

lation, and as such it is inherently very difficult to detect, as the presence of corrosion

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1. Introduction

(a) The ruptured gas line (b) One of the separated sections

Figure 1.1: On the 29th September 2008 a high pressure gas pipeline ruptured at Prudhoe

Bay, causing a release of natural gas into the atmosphere, and launching two sections of

pipe into the air to land 900 feet away from the incident [3].

is obscured by the insulation system. Because the corrosion develops undetected,

it can lead to serious pipeline failures, which have several adverse consequences in-

cluding the risk to the safety of site personnel, damage to the environment, and an

economic impact in terms of the cost of cleaning up any spillage and lost production.

Therefore, a significant proportion of the large maintenance budgets allocated by

operating companies are spent on the inspection for, and mitigation of, CUI [4,5].

1.1 Mechanism of Corrosion Under Insulation

Pipelines and vessels are thermally insulated primarily for two reasons. The first of

which is for process reasons, specifically, to maintain the hot temperatures present

in hot processes, and to maintain the cold temperatures of cold processes. The

second reason is for personnel protection; site personnel can easily burn themselves

on accidental contact with hot process pipework. The thermal insulation is pro-

tected from the environment by a layer of metallic weatherproofing cladding, which

is intended to keep the insulation dry, as insulation loses much of its effectiveness

once it becomes wet. The cladding material is usually galvanised steel, aluminium,

aluminised steel or stainless steel, in sheet form with a thickness in the range of 0.5

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1. Introduction

to 1.25 mm [5, p.120]. Joints between the different layers and sections of cladding

are typically sealed with mastic or silicon based sealants in order to prevent water

ingress. However, these sealants degrade over time, through exposure to the envi-

ronment, leading to the formation of a path for water ingress into the insulation.

A section of wet insulation creates an area on the steel pipe’s surface which is in

contact with water and a plentiful supply of oxygen, both of which are required

for corrosion to initiate. The corrosion rate of steel, assuming the presence of wa-

ter and oxygen, is primarily controlled by temperature [4, p.174], with increasing

temperatures causing increased rates of corrosion. The elevated temperature of the

insulated pipe creates an environment in which corrosion can proceed at a rapid rate

once water comes into contact with the steel of the pipe, with loss of wall thickness

occurring at a rate ranging from 0.3 to 2.2 mm per year [6–8].

Different types of corrosion occur depending on the material of the pipe. On carbon

steel (in which the primary alloying ingredient is carbon) and low-alloy steels (with

a chromium alloying percentage of less than 11 % [5, p.33]) the problem is corrosion

of the external surface of the pipe, leading to a loss in wall thickness and pitting.

On austenitic stainless steel pipes, conventional corrosion is no longer the problem,rather it is chloride external Stress Corrosion Cracking, referred to as SCC. If chlo-

ride ions are present in the water which is in contact with the austenitic stainless

steel pipe’s surface, then SCC may initiate, causing a fine network of transgranular

cracking to manifest, both on the surface and in the bulk of the material [4, p.175].

Chloride ions can be introduced into the insulation due to the testing of fire deluge

systems that use seawater, or due to being located in a coastal or marine environ-

ment, or through the leaching of contaminants from the insulation materials them-selves. In addition to the requirements for water and chloride ions, SCC requires

tensile stresses to exist in the component, therefore if the tensile stress can be elimi-

nated then SCC can be prevented [4, p.176]. Despite the distinct natures of the two

main forms of corrosion under insulation that can occur on different pipeline ma-

terials, water is a necessary precursor to both forms of corrosion, therefore if water

can be eliminated from the system then both forms of corrosion can be controlled.

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1. Introduction

The purpose of the weatherproofing barrier formed by the cladding is primarily

to protect the insulation and to keep the insulation dry, however, it would be im-

practical to attempt to create a barrier which would prevent any contact of the air

(and inherent water vapour) with the annular space occupied by insulation, as this

would require seals equivalent to a pressure vessel [4, p.174]. Therefore, temperature

changes (due to cyclic processes or variations in the environment) cause the cladding

and insulation system to breathe, allowing the ingress of water vapour. The ingress

of water is further hastened as the condition of the cladding degrades over time,

through mechanical damage (primarily caused by foot traffic), and deterioration of

the sealants.

The principal sources of water are deluge systems, rainwater, process liquid spillage

and condensation of water vapour [5, p.2]. Sites which are commonly reported to be

locations of CUI problems are mid-span insulation joints and saddle supports, with

joints at saddles leading to an even higher incidence of CUI. Vertical risers are also

problematic, as they shed water which tends to collect at insulation joints at the

bottom of the riser. Another situation which is very likely to lead to CUI problems

is an area of exposed pipe on an insulated line, which can occur due to improperreinstatement of insulation following inspection or maintenance procedures, as this

will readily allow water ingress into the exposed insulation [9, p.18]. Other sites

which are problematic are those areas of pipelines which are subject to cyclic tem-

peratures, with the lowest temperature at a value below the dew point, varying to

temperatures above the ambient [4, p.174]. This causes water to condense on the

pipe during the low temperature phase, which then allows corrosion to initiate as

the temperature increases. The rate of the corrosion reaction will increase as thetemperature of the pipeline increases to its maximum operating value. Even if this

maximum temperature is sufficiently high to bake off the water inside the insulation,

there still exists a transition period within which the pipe is both warm and wet,

providing ideal conditions for CUI to occur. For corrosion of carbon and low-alloy

steels, the range of temperatures of piping within which the majority of all CUI

cases occur is from −4 ◦C to 120 ◦C [10], although pipes with operating tempera-

tures down to −18 ◦C can suffer from CUI if they have intermittent flow resulting in

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33/192

1. Introduction

pipe, and then subsequently reinstated, a process which is prohibitively expensive

and time consuming [5, p.47].

Pulse-echo ultrasonic measurements can be made to determine the wall thickness

at a point. This either requires complete removal of the insulation or requires

cutting inspection windows, both of which are to be avoided for reasons previously

stated. The advantage of this technique is that it gives the remaining wall thickness

accounting for both external and internal corrosion, but the disadvantage is the

difficulty of getting a reading on a corroded surface thus requiring significant surface

preparation [5, p.47].

Several radiographic techniques exist, such as: profile radiography, digital radiog-

raphy, flash radiography and real-time radiography. These are all techniques which

use either x-rays or gamma rays to image the profile of the pipe or to provide in-

formation about the wall thickness of the internal pipe. Their main advantage is

the ability to perform the inspection without the need to remove the insulation, and

can be used with the pipe in-service. The main disadvantages are the strict safety

requirements associated with ionising radiation, and the small area of inspection

leading to slow rates of coverage or, if a sampling approach is adopted, the risk of

missing problem areas [5, p.49].

A technique which can be used to comprehensively and rapidly inspect long lengths

of pipeline around the entire circumference from a single inspection position is the

guided wave ultrasonic technique. This technology involves fitting a ring-array of

transducers around the pipe at one position. These transducers excite the propaga-

tion of low-frequency ultrasonic signals down the length of the pipeline. Any defects,such as cracks or corrosion, give rise to reflections of the incident signal, which return

to the transducer array, allowing the detection of these defects. Several commer-

cially available guided wave inspection systems have been developed [12, 13]. The

advantages of guided ultrasonic waves include the ability to inspect long lengths of

pipeline (25 m in each direction from a single array position [14]) about the entire

circumference of the pipe, which is preferable to the spot testing of other techniques

such as conventional ultrasound or radiographic methods. Another advantage is that

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1. Introduction

this technique inspects the pipeline with the insulation still in place, with the excep-

tion of a small length required to fit the transducer array. However, the technique

requires an existing loss in wall thickness due to corrosion, before it can highlight

areas which are at risk from CUI.

Pulsed eddy current inspection is another means of inspecting for corrosion under

insulation; it is a method that is designed to measure the remaining wall thickness

of the pipe with the cladding and insulation in place. This technique uses a direct

current in a coil placed onto the cladding to create a stable magnetic field within

the pipe under the insulation. The current in the coil is then switched off, creating

eddy currents within the pipe. The time taken for these eddy currents to dissipate

is related to the thickness of the metal and can therefore be used to measure the

average remaining wall thickness in that area. The advantages are that it can be

used without altering the insulation system in any way, and with the pipeline in-

service. The disadvantages are the limited inspection area, and an inability to detect

localised corrosion, and it is restricted by an inability to inspect a pipe through steel

cladding [5, p.135].

A technique which takes an indirect approach to tackling the problem of CUI is that

of the neutron backscattering technique. This method uses high energy neutrons

emitted by a radioactive source to inspect the insulation, through the cladding, for

the presence of water. Water will attenuate the energy of the neutrons, therefore the

reflected neutrons will be of a lower energy if there is water present. The detection

of low energy neutrons indicates the presence of water at that position, with the

number of low energy neutrons detected being proportional to the amount of water

present [10]. The advantages include the ability to perform the inspection with

the pipeline in-service, and without removing any insulation; but the disadvantages

include the safety requirements of the radioactive source, the limited inspection area,

and the requirement to confirm corrosion with an additional inspection method such

as x-ray or gamma radiography [5, p.50].

Another technique which detects water instead of the corrosion itself is infrared

thermography. The premise is to use a thermographic camera to inspect the pipeline,

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1. Introduction

and areas of wet insulation will appear hotter than areas of dry insulation due to

the reduced effectiveness of the wet insulation resulting in hot-spots on the pipeline.

The increased safety and the speed of coverage of this technique eliminates the major

disadvantages of neutron backscattering, however, the sensitivity and accuracy of the

technique suffer, since only significant water volumes are detectable, and hot-spots

can be caused through other means besides wet patches [5,10].

1.3 The Premise for the Use of Microwaves for

the Detection of CUI

As discussed in Section 1.2, the infrared thermographic and neutron backscattering

techniques are distinct from the other inspection methods in that they aim to detect

the water which causes the corrosion rather than the presence of active corrosion

itself. This is an advantageous approach as it gives a much earlier indication of

areas of a pipe that are likely to suffer from CUI, allowing sufficient time to mitigate

the problem. However, the two techniques that are currently in use and capable

of detecting water have serious limitations as discussed in Section 1.2; therefore, it

would be beneficial to be able to use a long-range screening technique to monitor a

length of pipeline for the first ingress of water into the insulation. This would provide

an early warning of the likely occurrence of CUI and prompt remedial action to reseal

the cladding, thereby preventing corrosion from initiating.

Microwave frequency techniques are seeing increased application in the field of NDE.

A common use is to determine the strength of concrete structures by measuring the

material properties using microwaves, including the water-to-cement ratio and the

presence of Sodium Chloride [15–20]. Another application is that of the inspection

of metallic surfaces for thin cracks using microwave probes [21–25]. A third area in

which microwaves are being successfully used is that of the inspection for disbonds

in layered dielectric composite materials [26–30]. However, the inspection technique

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1. Introduction

Figure 1.2: The structure of a clad and insulated pipeline can be used as a large coaxial

waveguide to support the propagation of electromagnetic waves. The microwave regime is

of particular interest due to the sensitivity of these frequencies to the presence of water,

raising the possibility of being able to detect the first ingress of water into the insulation,

allowing the initiation of corrosion to be prevented.

described in this thesis takes a fundamentally different approach to other forms of

microwave NDE.

The technique which is the subject of this thesis is based on the premise that a

pipeline which has been fitted with thermal insulation and metallic cladding is ef-

fectively a scaled-up version of a coaxial cable, with the inner conductor formed by

the pipeline, the outer conductor formed by the cladding, and the thermal insulation

layer acting as the dielectric within the coaxial cable, as shown in Figure 1.2. In this

manner, the pipeline can be used as a coaxial waveguide to support the propagation

of electromagnetic waves [31]. The premise for the technique is to excite microwave

propagation down the length of the pipeline with the use of an antenna-based ex-

citation system inserted into the insulation. If the cladding has become damaged

and allowed the ingress of water, then this patch of wet insulation will give rise to

a reflection of the incident microwave signal. The reflected signal returns to the

exciting antenna, where it is received, and used to detect the presence of water

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1. Introduction

Input Signal Water Volume

Pipeline Contents

Incident Signal Transmitted SignalReflected Signal

Figure 1.3: Antennas are inserted into the insulation layer, exciting microwave propa-

gation down the length of the pipeline. Water volumes in the insulation act as impedance

discontinuities, giving rise to a partial reflection of the incident signal which can be used

to detect and locate wet sections of insulation along the length of the pipeline.

within the waveguide, and also to determine its position. This process is illustrated

in Figure 1.3.

One of the reasons why microwave frequencies are of particular interest is the trans-

parency of the insulation material to electromagnetic waves at these frequencies, so

the inspection signal will experience very little attenuation. A second reason for

considering electromagnetic waves in the microwave regime is the high value of the

relative permittivity of water at these frequencies [32, p.315]. A high value for the

relative permittivity is beneficial as it means that water will affect the impedance

of the waveguide to a greater extent thus giving rise to a stronger reflection. This

is because the characteristic impedance, Z 0, of a coaxial waveguide is given by the

equation

Z 0 = 1

2π

ln ab µ0µr

0r, (1.1)

where a and b are the radii of the outer and inner conductors respectively, and

the material properties of the medium filling the waveguide are given by: the vac-

uum permeability, µ0; the relative permeability, µr; the vacuum permittivity, 0;

and the relative permittivity, r [33, p.198]. It can be seen from this equation that

the characteristic impedance varies with the relative permittivity of the material as

Z 0 ∝ 1/√ r. We can assume that dry insulation has a relative permittivity equiva-

lent to air, r = 1, (the validity of this assumption will be discussed in Section 3.1.1)

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1. Introduction

and we can take the value of the relative permittivity of water to be r = 79.7 at

1 GHz according to values given in [34]. A typical example of a pipeline specifica-

tion would be a 6 ” Nominal Pipe Size (NPS), equivalent to an outer diameter of

6.625” = 168.2 mm, giving a value for the inner radius of b = 84.1 mm. Typically,

this pipeline would be fitted with thermal insulation with a thickness of 3 ”, giving

an outer radius of a = 160.3 mm. We can calculate the impedance of this pipeline

when dry to be Z 0dry = 38.7 Ω, and if water has saturated the insulation across the

entire cross-section then the impedance will be Z 0wet = 4.33 Ω. The reflection coeffi-

cient, Γ, experienced by a signal incident on such a boundary between wet and dry

insulation can be obtained with the simple analytical relationship [35, p.29] given

by

Γ =Z 0wet − Z 0dryZ 0wet + Z 0dry

=

√ rdry −

√ rwet√

rdry +√ rwet

, (1.2)

which gives Γ = −0.80. Therefore, if water breaches the cladding and fully saturatesthe insulation, then the boundary between the dry section of insulation and the wet

patch will cause a reflection of 80 % of the incident signal back to the excitation

antenna. Whilst a fully saturated insulation cross-section is not unusual, the first

sign of water ingress will be the presence of water collecting at the 6 o’clock position

within the cladding and gradually saturating the lower portion of the insulation,

therefore presenting a smaller impedance discontinuity, and thus causing a smaller

reflection. Chapter 6 of this thesis will discuss the sensitivity of the technique to the

presence of water, including a measurement of the minimum cross-sectional extent

of water that can be detected.

1.4 Similar Techniques

The principle of using the structure of the pipeline as a coaxial waveguide to sup-

port electromagnetic wave propagation was first proposed by Burnett and Frost,

who developed a technique that is now marketed by Profile Technologies Incorpo-

rated (PTI). The general approach is described in patents [36,37] and the paper [38].

These indicate that the technique propagates electromagnetic waves in the radiowave

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1. Introduction

regime within the coaxial waveguide. However, the literature does not explain the

details of how the technique operates, how the excitation system functions, nor does

it provide sufficient quantitative evidence to determine the practical feasibility of

the method. One potential disadvantage of the PTI implementation of the coaxial

waveguide idea is that operating at the low frequencies of the radiowave regime is

likely to lead to poor spatial resolution of waveguide features. The lack of data

available to assess the feasibility of the PTI technique, its advantages and disadvan-

tages, and its boundaries of operation, means that very little can be gained from the

existence of such a technique in terms of scientific contributions to the development

of a higher frequency guided microwave technique.

1.5 Outline of the Thesis

The objective of this thesis is to determine the feasibility of using guided microwaves

to inspect the insulation layer of clad and insulated pipelines for the presence of

water. This fundamental goal will be divided into subsidiary objectives, which will

be covered as separate chapters within the thesis.

In order to provide some context for the scientific discussion within this thesis, the

theoretical background to this work is discussed in Chapter 2. This will include the

use of Maxwell’s equations, and the analytical solution for electromagnetic waves

propagating in rectangular waveguides. This represents a much simpler situation

than a coaxial waveguide and is therefore ideal for introducing the properties of

guided waves, such as dispersion and modal field distributions. This chapter willalso introduce the numerical modelling technique which is used throughout this work

to support the theoretical and experimental research.

The first objective of the thesis will be determining which modes propagate in the

large coaxial waveguides formed by insulated pipelines and whether they can be

used for inspection. This will be covered in Chapter 3 by examining the dispersion

properties of the coaxial waveguide. This will include a description of the analytical

model used to describe propagation in coaxial waveguides, and the results obtained

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1. Introduction

from this model; specifically the dispersion properties of the propagating modes and

their modal field distributions.

Chapter 4 will discuss the development of the design of the antenna array used

to excite guided microwave propagation in insulated pipelines. This will include a

discussion of the significance of impedance matching at the antenna array, and a

review of potential methods of improving the impedance match. The chapter will

present a numerical study to optimise the antenna design in order to maximise energy

transmission into the various coaxial waveguide dimensions formed by pipelines of

typical industrial specifications.

Experimental validation of the guided microwave technique, and the optimised exci-

tation system, is sought in Chapter 5. The experimental setup used in the laboratory

to model insulated pipelines is described. This model experimental setup is also used

to measure the effect on the microwave signal of some of the types of insulation that

are commonly fitted to pipelines. Finally, this chapter will present results from a

field test, which was conducted to validate the use of the model experimental setup

in representing real pipeline conditions.

An issue of central importance to the performance of the guided microwave tech-

nique is the sensitivity with which it can detect water volumes within the waveguide.

Chapter 6 describes an investigation to assess this sensitivity using numerical simu-

lations and experiments in the laboratory. In addition, the chapter presents results

from a realistic inspection scenario conducted during a field test on a section of real

industrial pipeline.

Bends are a common feature on industrial pipelines. As such, the value of an inspec-

tion technique will be dependent on its ability to maintain its performance in the

presence of common features such as bends. Chapter 7, therefore, presents numeri-

cal work to understand the behaviour of guided microwaves at bends. Experimental

results are obtained to validate the numerical findings.

Another common feature of pipelines are pipe supports. Chapter 8 describes an

investigation to quantify the reflection and transmission properties of pipe supports

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1. Introduction

in order to determine whether the guided microwave technique can be used to inspect

beyond typical pipe supports.

A review of the thesis is provided in Chapter 9, followed by a summary of the main

findings of the research. The thesis concludes with a discussion of some potential

areas for future work, which would bring the technique closer to field application.

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Chapter 2

Theoretical Background

The introductory chapter described the motivation for this project including the

mechanism of corrosion under insulation. The current NDE techniques for the

detection of CUI were reviewed including the reasons why this form of corrosion

continues to be such a significant and ongoing problem. The premise for the use

of guided microwaves to inspect the insulation layer of pipelines for the presence

of water was described including the use of the structure of a clad and insulated

pipeline as a coaxial waveguide to support electromagnetic wave propagation.

In order to understand the importance of several aspects of guided wave propagation,

this section will present some of the relevant background theory. This will begin with

Maxwell’s equations, followed by the boundary conditions which exist at the walls

of a waveguide, which allow them to guide electromagnetic waves. Before dealing

with coaxial waveguides, the relatively simple case of a rectangular waveguide will

be presented, including introducing the use of dispersion curves and concepts such

as modes of propagation and field distributions.

In addition, this section will explain the necessity for numerical techniques to study

complex problems and introduce the particular numerical technique which was used

throughout this project. Following on from this, the theory for the method of signal

analysis for locating impedance contrasts in a transmission line will be introduced,

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2. Theoretical Background

accompanied by the manner in which the resolution of features in the waveguide can

be optimised.

2.1 Maxwell’s Equations

Maxwell’s equations form the basis for the background theory describing the prop-

agation of electromagnetic waves in waveguides. The equations are given by

∇ · D = Q∇

·B = 0

∇× E = −∂ B∂t

(2.1)

∇× H = ∂ D∂t

+ J,

where D is the electric flux density; Q is the free charge density; B is the magnetic

flux density; E is the electric field; H is the magnetic field; and J is the conduction

current density. D is related to E by D = 0rE, where 0 and r are the vacuum

and relative permittivities of the dielectric material, respectively; whilst B is relatedto H by B = µ0µrH, where µ0 and µr are the vacuum and relative permeabilities

of the dielectric material, respectively. Maxwell’s equations can be used to describe

the propagation of uniform plane electromagnetic waves in a simple medium within

which there are no free charges and currents, therefore Q = 0 and J = 0 [39, p.132].

If we assume a sinusoidal time variation of the form e jωt, where ω is the angular

frequency and t is time, then we can write ∂/∂t = jω . This gives us Maxwell’s

equations in the form given in [33, p.118] as

∇ · D = 0∇ · B = 0∇× E = − jωB (2.2)∇× H = jωD.

A point-source of electromagnetic waves in free-space will create waves propagating

in all directions, as such the intensity on this spherical wavefront will attenuate

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according to the inverse-square law. In order to achieve transmission with lower

attenuation, it is possible to confine the waves to travel in a particular direction

with the use of a guiding physical structure. Such a guiding structure is known

as a waveguide , and for electromagnetic waves, these usually take the form of an

interface between a conductor and a dielectric. One example of an electromagnetic

waveguide is the rectangular waveguide, which consists of a hollow metallic tube with

a rectangular cross-section. The electromagnetic waves are confined by the metallic

walls of the waveguide and are able to propagate with relatively low attenuation. It

is the boundary conditions that exist at the interface between the conductor and the

dielectric that allow these structures to guide the passage of electromagnetic waves.

The first boundary condition of a conductor-dielectric interface is that the tangen-

tial component of the electric field is continuous across the boundary, and since

E = 0 inside a perfect conductor, the electric field inside the dielectric must be

perpendicular to the interface between the dielectric and the conductor. The second

boundary condition is that the normal component of the magnetic flux density is

continuous across the boundary. From the third of Maxwell’s equations in (2.2),

and since E = 0 inside a perfect conductor, it can be seen that B = 0 inside aperfect conductor. Therefore, the normal component of B, and hence H, inside the

dielectric must be zero at the interface. As a consequence of these two conditions,

in proximity to the surface of the conductor, the electric field within the dielectric

must be oriented in a direction normal to the surface, and similarly the magnetic

field must be oriented in a direction that is tangential to the surface.

These are the only boundary conditions required to solve Maxwell’s equations for

the case of a rectangular waveguide, however, for the more complex case of the

coaxial waveguide, an additional condition exists. Due to the circular nature of this

waveguide, the electric and magnetic fields at θ and θ + 2π must be equal, as this is

the same point in space.

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2.2 Analytical Solution for the Rectangular

Waveguide

Before looking at the complex case of coaxial waveguides, it is beneficial to first

study the relatively simple case of electromagnetic wave propagation in a rectangular

waveguide.

x

y

w

h

z

Figure 2.1: Cross-sectional view of a rectangular waveguide. The dimensions of the

waveguide are denoted by w for the width, and h for the height.

The rectangular waveguide case has greater simplicity because the characteristic

equation, which describes how the wave propagates, is explicit; characteristic equa-

tions are usually implicit and often difficult to solve. The characteristic equation for

the rectangular waveguide is given by

β 2 = ω20µ0rµr − p2π2

w2 − q

2π2

h2 , (2.3)

where β is the phase constant of the guided wave; ω is the angular frequency andis related to the frequency, f , by ω = 2πf ; w and h are the width and height of

the waveguide, respectively, as shown in Figure 2.1; and p and q are integers. By

assigning integer values to p and q in the characteristic equation, all the permitted

values of β can be found. Each combination of p and q refers to a distinct mode of

propagation within the waveguide [33, p.212].

If β 2 is positive, then there are two real roots given by

±β , with the sign indicating

the direction of propagation relative to the z -axis. If β 2 is negative, then there are

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two imaginary roots at ± jβ ; such imaginary phase constants are said to be cutoff,with the resultant wave being referred to as an evanescent wave. Evanescent waves

are not capable of propagating; their amplitude decays exponentially with z . The

one remaining possibility is for β 2

= 0. The frequency at which this occurs is known

as the cutoff frequency, f c, and is dependent on the dimensions of the waveguide

and the p and q values of the particular mode. The cutoff frequency for rectangular

waveguide modes is given by

f c =

1

40µ0rµr

p2

w2 + q 2

h2

. (2.4)

For any given mode in a particular waveguide, at frequencies below the cutoff fre-

quency β 2 is negative and the mode is evanescent, whereas as the frequency increases

above the cutoff, β 2 becomes positive and the mode begins to propagate within the

waveguide. The mode whose cutoff occurs at the lowest frequency is said to be

the lowest mode , with modes that begin to propagate at higher frequencies being

referred to as higher order modes .

There are two velocities of significance when dealing with the propagation of waves;

these are the phase velocity, ν p, and the group velocity, ν g. The phase of the wavetravels at the phase velocity; for example, the tip of a particular peak in a wavepacket

will travel at this speed. The phase velocity is often much greater than the speed

of light. The group velocity refers to the speed at which the envelope of the wave

travels; this is the speed at which information is carried by the wave, and does not

exceed the speed of light. The expressions for the phase and group velocity are

ν p = ω

β (2.5)

ν g = ∂ω

∂β . (2.6)

The characteristic equation in (2.3) can be used in conjunction with the expressions

in (2.5) and (2.6) to plot the relationship between the wave velocities and the fre-

quency; these are known as dispersion curves. Figure 2.2 displays the dispersion

curves of the phase and group velocities, normalised to the speed of light in vacuum,

c0, for some of the lower modes in a rectangular waveguide.

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1010

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

TE0q

TE1q

TE2q

TE3q

TE4q

Phase velocity dispersion curves

Frequency (Hz)

N o r m a l i s e d p h a s e v

e l o c i t y

TE04

TE03

TE02

TE01

TE14

TE13

TE12

TE11

TE10

TE24TE23TE22TE21TE20

TE34

TE33

TE32

TE31

TE30

TE44

TE43

TE42

TE41

TE40

3.15 GHz 6.31 GHz

1010

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TE0q

TE1q

TE2q

TE3q

TE4q

Group velocity dispersion curves

Frequency (Hz)

N o r m a l i s e d g r o u p v e l o c i t y

TE04

TE03

TE02

TE01

TE14

TE13

TE12

TE11

TE10

TE24

TE23

TE22

TE21

TE20

TE34

TE33

TE32

TE31

TE30

TE44

TE43

TE42

TE41

TE40

Figure 2.2: Phase and group velocity dispersion curves, normalised to the speed of light

in vacuum, for some of the lower modes in a G band rectangular waveguide (dimensions

of w = 47.5 mm and h = 22.1 mm and a frequency range of 3.95 to 5.85 GHz bandwidth).

Each of the curves in Figure 2.2 represents a separate mode of propagation within

the waveguide, and they are labelled according to the standard mode nomenclature

for rectangular waveguides. There are in fact two series of modes, referred to as:

Transverse Magnetic (TM) modes, with H z = 0; and Transverse Electric (TE)

modes, with E z = 0. However, for the rectangular waveguide, the phase constant

of a TM mode is equal to the phase constant of the equivalent TE mode, therefore

only the TE modes are plotted in Figure 2.2. Waldron [33] prefers to refer to the TE

and TM modes as H and E modes, respectively, however, the TE and TM notation

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is the one that is used predominantly in the field [35, 39–41]. The numbers in the

subscript of the mode refer to the p and q values for that mode, i.e. TE pq and TM pq,

and denote the periodicity of the variation of the field in the x and y directions

respectively. It can be seen that all of the modes are highly dispersive, with their

phase and group velocities being highly dependent on the frequency. The phase

velocities are always greater than the speed of light in the medium, c, whilst the

group velocities are always less than c, but both are asymptotic to c. It can be

shown that the phase and group velocities are related by the expression

ν g ≤ c√ rµr

≤ ν p, (2.7)

or, in another form

ν pν g = c2

rµr. (2.8)

In order to maximise the performance of an inspection system, it is necessary to

maximise the signal-to-coherent-noise ratio (SCNR). Coherent noise refers to any

deterministic signals that corrupt the signal of interest and cannot be removed by

temporal averaging. One aspect of using guided waves for inspection, which has an

adverse effect on the SCNR, is the fact that modes propagating within waveguides

often undergo dispersive propagation. It was seen in Figure 2.2 that all of the modes

are highly dispersive. This has the effect that a wavepacket will undergo temporal

spreading as it propagates, due to each of the frequency components inside the

wavepacket travelling at different phase velocities. This temporal spreading causes

a reduction in the amplitude of the signal, which adversely effects the SCNR.

Another aspect of guided wave propagation which can adversely effect the SCNRis the fact that a waveguide is capable of supporting an infinite number of modes

of propagation. If there are multiple modes propagating, each of the modes will

travel at a different group velocity, and undergo varying degrees of dispersion. Con-

sequently, the propagating modes will become out-of-phase with each other and

undergo complicated interference processes. The result will be a signal which is im-

possible to interpret due to the multitude of reflections and the high level of coherent

noise due to interference effects. It is for this reason that it is desirable to excite

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a signal within the waveguide which contains only a single mode; this is known as

pure mode excitation.

From Figure 2.2 it can be seen that there is a narrow frequency range within which

there is only the TE10 mode that is capable of propagating, before the TE20 begins

to propagate, i.e. from 3.15 to 6.31 GHz. Rectangular waveguides come in a range

of standard sizes, which are referred to as R band, D band, S band, etc. The

dimensions of these standard rectangular waveguides are strictly controlled in order

to gain maximum utility from this pure mode region, and hence each waveguide has

a defined operating frequency range. Figure 2.2 displays the dispersion curves for a

G band rectangular waveguide, which has an operating frequency range of 3.95 to

5.85 GHz. The lower limit of the operating frequency range (3.95 GHz) is somewhat

higher than the cutoff frequency of the TE10 mode (3.15 GHz), this is in order to

operate the waveguide in the region of the dispersion curve which is flattest and

hence least dispersive. The upper limit of operating frequency range 5.85GHz is

also slightly lower than the cutoff frequency of the TE20 mode (6.31 GHz), and this

is in order to avoid interference from the evanescent TE20 mode, an effect which

becomes greater the closer the operating frequency is to the cutoff frequency.

For comparison, the phase velocity dispersion curves of an R band and an S band

rectangular waveguide are plotted in Figure 2.3. It can be seen that as the size of

the waveguide decreases, the cutoff frequencies of the various modes increase, and

consequently the waveguide can be used for operations in a higher frequency range.

It is very useful to be able to visualise the distribution of the electric and magnetic

fields within the waveguide for each of the modes which are capable of propagating.Equations known as the field components of the waveguide allow the Cartesian

components of the electric and magnetic fields to be calculated. Waldron [33, p.224]

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gives the field components for TM modes in rectangular waveguide as

E x = pλ20w√ whr

2β̄ µ0/0

rµr − β̄ 2 cos kxx sin kyy

E y = qλ20

h√ whr

2β̄ µ0/0

rµr − β̄ 2 sin kxx cos kyy

E z = j2√

2λ0√ whr

rµr − β̄ 2β̄ 0/µ0

sin kxx sin kyy (2.9)

H x = −qλ20h√ wh

2r

0/µ0

β̄ rµr − β̄ 2

sin kxx cos kyyH y =

pλ20w√ wh

2r

0/µ0

β̄ rµr − β̄ 2

cos kxx sin kyy

H z = 0,

where the Cartesian components of the wavenumber vector are given by kx =

p2π2/w2, and ky = q 2π2/h2; and β̄ is the phase constant normalised to that of

vacuum, i.e. if λ0 and λwg are the wavelengths in vacuum and inside the waveguide

respectively, then β̄ = λ0/λwg = λ0β/2π. The field components for TE modes are

E x = −qλ2

0

h√ wh

2µr

µ0/0

β̄ rµr − β̄ 2

cos kxx sin kyyE y =

pλ20w√ wh

2µr

µ0/0

β̄ rµr − β̄ 2

sin kxx cos kyyE z = 0

H x = − pλ20w√ whµr

2β̄ 0/µ0

rµr − β̄ 2 sin kxx cos kyy (2.10)

H y = qλ2

0

h√ whµr

2

¯β 0/µ0

rµr − β̄ 2 cos kxx sin kyy

H z = j2√

2λ0√ whµr

rµr − β̄ 2β̄ µ0/0

cos kxx cos kyy.

These field components allow the field distributions to be plotted across a cross-

section of the rectangular waveguide for each of the modes. Figure 2.4 displays the

electric and magnetic field distributions for nine of the lowest modes in rectangular

waveguides. These are in good agreement with the field distributions plotted in

[33,39,41,42].

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E field of TE10

H field of TE10

(a) TE10

E field of TE20

H field of TE20

(b) TE20

E field of TE01

H field of TE01

(c) TE01

E field of TE11

H field of TE11

(d) TE11

E field of TM11

E field of TM11

(e) TM11

E field of TE21

H field of TE21

thesis_2012_09_07_final_must read.pdf

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